Optymalizacja kształtu dynamicznych zagadnień kontaktowych

Andrzej Myśliński

This paper deals  with  the numerical solution of   a  shape  optimization  problem  of  a viscoelastic body in unilateral dynamic contact with a rigid foundation  The heat generation due to friction is taken into account. The shape optimization  problem  consists in finding, in a contact region, such a shape  of the boundary of the domain occupied by the body that  the  normal contact stress is minimized.  The volume of the body is assumed constant.  In this paper, the necessary  optimality condition for this optimization problem is formulated. Numerical algorithm for solving the optimal conditions system for this optimization problem is based on   application of the level set methods. The speed vector field driving the propagation of the level set function is given by the Eulerian derivative of an appropriately defined  functional with respect to the free boundary.  The Eulerian derivative is calculated using the material derivative approach.  Numerical examples are provided.

Słowa kluczowe: level set methods, shape optimization, dynamic contact problem

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